smoke domain, original object material, how to make it show through smoke: AOQ
Just to remove this from Unanswered Questions, I am answering it myself.  Turns out it was a dumb question anyway.

Point 1:  when textures look weird and you are using BI, check the World carefully for environmental lighting.  This was 90 percent of my problem, just dumb n00b error.

Point 2:  the smoke effect seems to reveal more of the cube surfaces when I make the proportion of Volume smoke higher and the proportion of Face smoke lower, unsurprisingly.  Tweaking this enabled me to get pretty much the look I wanted.